Information on Result #1070575
Linear OOA(12842, 4097, F128, 4, 21) (dual of [(4097, 4), 16346, 22]-NRT-code), using OOA 4-folding based on linear OA(12842, 16388, F128, 21) (dual of [16388, 16346, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(12842, 16390, F128, 21) (dual of [16390, 16348, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(12841, 16385, F128, 21) (dual of [16385, 16344, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(12837, 16385, F128, 19) (dual of [16385, 16348, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(12853, 4247, F128, 4, 21) (dual of [(4247, 4), 16935, 22]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12855, 4289, F128, 4, 21) (dual of [(4289, 4), 17101, 22]-NRT-code) | [i] | ||
| 3 | Digital (21, 42, 4097)-net over F128 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |